Recoil effects in a quantum theory of the skyrmion

The purpose of this work is to illustrate how the Kerman-Klein method of quantization, introduced originally for the restoration of broken symmetries in the non-relativistic many-body problem and later utilized by Goldstone and Jackiw (1975) for a one-dimensional soliton, can be applied to the study of Skyrmion physics. In this method, one replaces the piecemeal quantization of collective coordinates by a formal canonical quantization of a full classical Hamiltonian, collectivity arising from the structure of the associated Hilbert space. In this first account, the restoration of translational invariance is studied using a quantized form of the original Skyrme Hamiltonian. This involves the study of matrix elements of the Heisenberg equations of motion by means of the completeness relation in a restricted Hilbert space consisting of all possible momentum eigenstates of the Skyrmion. In the limit in which the ratio of the Compton wavelength of the Skyrmion to its size is negligible (corresponding to the large Nc limit of QCD), the resulting classical field equation properly describes a boosted hedgehog. Higher order terms in this ratio describe quantum recoil corrections to the Skyrmion mass. In contrast to (1+1)-dimensional field theories studied previously, a gradient expansion for the calculation of these corrections diverges. In a more careful evaluation, there is a finite but large contribution from the Skyrme term. The dependence of the result on the ordering ambiguities that occur in the quantization of the field kinetic energy is also described.